61cef96cd7
This PR gives a proof of `LawfulToForwardSearcherModel` for `Slice` patterns, which amounts to proving that our implementation of KMP is correct. Note that this PR also changes the KMP implementation to make it slightly more efficient and easier to verify. I also have a correctness proof for the old implementation, so there were no bugs in the old implementation.
39 lines
2 KiB
Text
39 lines
2 KiB
Text
module
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inductive S where
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| m (b e : Nat)
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| r (b e : Nat)
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deriving Repr, BEq, DecidableEq
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def run (s pat : String) : List S :=
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String.Slice.Pattern.ForwardSliceSearcher.iter pat.toSlice s.toSlice
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|>.map (fun | .matched b e => S.m b.offset.byteIdx e.offset.byteIdx | .rejected b e => S.r b.offset.byteIdx e.offset.byteIdx)
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|>.toList
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-- 𝔸 is [240,157,148,184]
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-- 𝕸 is [240,157,149,184]
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#guard run "aababaab" "a" = [.m 0 1, .m 1 2, .r 2 3, .m 3 4, .r 4 5, .m 5 6, .m 6 7, .r 7 8]
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#guard run "aab" "ab" = [.r 0 1, .m 1 3]
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#guard run "aababacab" "ab" = [.r 0 1, .m 1 3, .m 3 5, .r 5 6, .r 6 7, .m 7 9]
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#guard run "aaab" "aab" = [.r 0 1, .m 1 4]
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#guard run "aaaaa" "aa" = [.m 0 2, .m 2 4, .r 4 5]
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#guard run "abcabd" "abd" = [.r 0 2, .r 2 3, .m 3 6]
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#guard run "αβ" "β" = [.r 0 2, .m 2 4]
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#guard run "𝔸" "𝕸" = [.r 0 4]
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#guard run "𝔸𝕸" "𝕸" = [.r 0 4, .m 4 8]
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#guard run "α𝔸€α𝔸₭" "α𝔸₭" = [.r 0 9, .m 9 18]
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#guard run "α𝔸𝕸α𝔸₭" "α𝔸₭" = [.r 0 6, .r 6 10, .m 10 19]
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#guard run "𝕸𝔸𝕸𝔸₭" "𝕸𝔸₭" = [.r 0 8, .m 8 19]
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#guard run "𝕸𝔸𝕸β₭" "𝕸𝔸₭" = [.r 0 8, .r 8 17]
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#guard run "𝔸𝔸𝔸𝔸𝕸𝔸𝔸𝔸𝕸" "𝔸𝔸𝕸" = [.r 0 4, .r 4 8, .m 8 20, .r 20 24, .m 24 36]
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#guard run "𝔸b" "𝕸" = [.r 0 4, .r 4 5]
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#guard run "𝔸bb𝕸β" "𝕸" = [.r 0 4, .r 4 5, .r 5 6, .m 6 10, .r 10 12]
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#guard run "𝔸bbββαβαββββ𝕸β" "ββ𝕸" = [.r 0 4, .r 4 5, .r 5 6, .r 6 8, .r 8 10, .r 10 12, .r 12 14, .r 14 16, .r 16 18, .r 18 20, .m 20 28, .r 28 30]
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#guard run "𝔸β𝕸" "𝕸" = [.r 0 4, .r 4 6, .m 6 10]
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#guard run "𝔸b𝕸xu∅" "𝕸x" = [.r 0 4, .r 4 5, .m 5 10, .r 10 14]
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#guard run "é" "ù" = [.r 0 2]
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#guard run "éB" "ù" = [.r 0 2, .r 2 3]
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#guard run "abcabdabcabcabcabe" "abcabdabcabe" = [.r 0 6, .r 6 9, .r 9 18]
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#guard run "abcabdabcxabcabdabcabe" "abcabdabcabe" = [.r 0 6, .r 6 9, .r 9 10, .m 10 22]
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#guard run "€α𝕸€α𝔸€α𝕸€α𝕸€α𝕸€αù" "€α𝕸€α𝔸€α𝕸€αù" = [.r 0 18, .r 18 27, .r 27 52]
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